Toric Hilbert schemes.

DOI10.1215/S0012-7094-02-11132-6zbMath1067.14005MaRDI QIDQ1847899

Irena Peeva, Michael Stillman

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

toric varietymultigrading

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Parametrization (Chow and Hilbert schemes) (14C05)

Related Items

Open problems on syzygies and Hilbert functions, The toric Hilbert scheme of a rank two lattice is smooth and irreducible., Quotients of an affine variety by an action of a torus, On the smoothness of lexicographic points on Hilbert schemes, Flips and the Hilbert scheme over an exterior algebra, Moduli of McKay quiver representations. II: Gröbner basis techniques, The main component of the toric Hilbert scheme, Moduli of affine schemes with reductive group action, Multigraded Hilbert schemes, Non-connected toric Hilbert schemes, Compactified Jacobians and Torelli map, The T-Graph of a Multigraded Hilbert Scheme, A point set whose space of triangulations is disconnected, Existence of unimodular triangulations — positive results, Stable reductive varieties. II: Projective case, Local equations for the toric Hilbert scheme

Uses Software

• Macaulay2

Cites Work

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• Deformation classes of graded modules and maximal Betti numbers
• Classification of \(A\)-graded algebras with 3 generators
• Syzygies of codimension 2 lattice ideals
• Local equations for the toric Hilbert scheme
• Complete moduli in the presence of semiabelian group action.
• Classification of generalized \(A\)-graded algebras with 3 generators
• Binomial ideals
• Connectedness of Hilbert scheme
• A-graded algebras and continued fractions
• On the Hilbert Scheme Compactification of the Space of Twisted Cubics
• Generic lattice ideals